Report on scipost_202411_00033v1

Abstract

We investigate why, in quantum many-body systems, the adiabatic fidelity and the overlap between the initial state and instantaneous ground states often yield nearly identical values.Our analysis suggests that this phenomenon results from an interplay between two intrinsic limits of many-body systems: the limit of small evolution parameters and the limit of large system sizes.In the former case, conventional perturbation theory provides a straightforward explanation.In the latter case, a key insight is that pairs of vectors in the Hilbert space orthogonal to the initial state tend to become nearly orthogonal as the system size increases.We illustrate these general findings with two representative models of driven many-body systems: the driven Rice-Mele model and the driven interacting Kitaev chain model.SciPost Physics Submission A.2 For time-evolved state 18 A.3 Various overlaps in perturbative expansion 20 B Non-interacting Hamiltonians 21 C Derivation of Eq. (41) 23 References 24

Authors 1

1. Vadim Cheianov Aachen Instituut-Lorentz

   Leiden University

   Affiliation as printed

   Instituut-Lorentz , Universiteit Leiden , P.O. Box 9506 , 2300 RA Leiden , The Netherlands